Skip to main content
SpringerLink
Log in

Parametric ranked set sampling

  • Estimation
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Ranked set sampling was introduced by McIntyre (1952,Australian Journal of Agricultural Research,3, 385–390) as a cost-effective method of selecting data if observations are much more cheaply ranked than measured. He proposed its use for estimating the population mean when the distribution of the data was unknown. In this paper, we examine the advantage, if any, that this method of sampling has if the distribution is known, for a specific family of distributions. Specifically, we consider estimation of μ and σ for the family of random variables with cdf's of the formF(x−μ/σ). We find that the ranked set sample does provide more information about both μ and σ than a random sample of the same number of observations. We examine both maximum likelihood and best linear unbiased estimation of μ and σ, as well as methods for modifying the ranked set sampling procedure to provide even better estimation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramowitz, M. A. and Stegun, I. A. (1968).Handbook of Mathematical Functions, National Bureau of Standards, Washington, D.C.

    Google Scholar 

  • Dell, T. T. and Clutter, J. L. (1972). Ranked set sampling theory with order statistics background,Biometrics,28, 545–555.

    Google Scholar 

  • Gore, S. D., Patil, G. P. and Sinha, A. K. (1994). Environmental chemistry, statistical modeling, and observational economy,Environmental Statistics, Assessment, and Forecasting (eds. C. R. Cothern and N. P. Ross), 57–97, Lewis Publishing/CRC Press, Boca Raton.

    Google Scholar 

  • Johnson, G. D., Patil, G. P. and Sinha, A. K. (1993). Ranked set sampling for vegetation research,Abstracta Botanica,17, 87–102.

    Google Scholar 

  • Lloyd, E. H. (1952). Least squares estimation of location and scale parameters using order statistics,Biometrika,39, 88–95.

    Google Scholar 

  • McIntyre, G. A. (1952). A method for unbiased selective sampling using ranked sets,Australian Journal of Agricultural Research,3, 385–390.

    Google Scholar 

  • Mosteller, F. (1946). On some useful inefficient statistics,Ann. Math. Statist.,17, 377–407.

    Google Scholar 

  • Muttlak, H. A. and McDonald, L. L. (1990). Ranked set sampling with respect to concomitant variables and with size biased probability of selection,Comm. Statist. Theory Methods,19, 205–219.

    Google Scholar 

  • Ogawa, J. (1951). Contributions to the theory of systematic statistics,Osaka Mathematical Journal,3, 175–213.

    Google Scholar 

  • Patil, G. P. and Taillie, C. (1993). Environmental sampling, observational economy, and statistical inference with emphasis on ranked set sampling, encounter sampling, and composite sampling,Bulletin ISI Proceedings of 49th Session, 295–312, Firenze.

  • Patil, G. P., Sinha, A. K. and Taillie, C. (1993a). Ranked set sampling from a finite population in the presence of a trend on a site,Journal of Applied Statistical Science,1, 51–65.

    Google Scholar 

  • Patil, G. P., Sinha, A. K. and Taillie, C. (1993b). Observational economy of ranked set sampling: comparison with the regression estimator,Environmetrics,4, 399–412.

    Google Scholar 

  • Patil, G. P., Sinha, A. K. and Taillie, C. (1994). Ranked set sampling,Handbook of Statistics Volume 12: Environmental Statistics (eds. G. P. Patil and C. R. Rao), 167–200, North Holland/Elsevier Science Publishers, New York and Amsterdam.

    Google Scholar 

  • Ridout, M. S. and Cobby, J. M. (1987). Ranked set sampling with non-random selection of sets and errors in ranking,Applied Statistics,36, 145–152.

    Google Scholar 

  • Sinha, Bimal K., Sinha, Bikas K. and Purkayastha, S. (1994). On some aspects of ranked set sampling for estimation of normal and exponential parameters,Statist. Decisions (in press).

  • Stokes, S. L. (1977). Ranked set sampling with concomitant variables,Comm. Statist. Theory Methods,6, 1207–1211.

    Google Scholar 

  • Stokes, S. L. (1980). Estimation of variance using judgment ordered ranked set samples,Biometrics,36, 35–42.

    Google Scholar 

  • Stokes, S. L. and Sager, T. W. (1988). Characterization of a ranked set sample with application to estimating distribution functions,J. Amer. Statist. Assoc.,83, 374–381.

    Google Scholar 

  • Takahasi, K. and Wakimoto, K. (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering,Ann. Inst. Statist. Math.,20, 1–31.

    Google Scholar 

  • Yanagawa, T. and Shirahata, S. (1976). Ranked set sampling theory with selective probability matrix,Austral. J. Statist.,18, 45–52.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management Science and Information Systems, University of Texas at Austin, CBA 5.202, 78712-1175, Austin, TX, USA

    Lynne Stokes

Authors
  1. Lynne Stokes
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper has been prepared with partial support from the United States Environmental Protection Agency under Cooperative Agreement Number CR821801-01-0. The contents have not been subjected to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.

About this article

Cite this article

Stokes, L. Parametric ranked set sampling. Ann Inst Stat Math 47, 465–482 (1995). https://doi.org/10.1007/BF00773396

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00773396

Key words and phrases

Search

Navigation